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In the following question, I agree that b is the correct answer, but why is "a" not also correct. The EWMA do not include the mean reversion term (i.e product of weight and long run variance). But does this not indirectly assume that the long run volatility/variance is zero in EWMA, therefore it is not included.

Which of the following statements about the exponentially weighted moving average (EWMA) model and the generalized autoregressive conditional heteroscedasticity (GARCH(1,1)) model is correct?

a. The EWMA model is a special case of the GARCH(1,1) model with the additional assumption that the longrun volatility is zero.

b. A variance estimate from the EWMA model is always between the prior day’s estimated variance and the

prior day’s squared return.

c. The GARCH(1,1) model always assigns less weight to the prior day’s estimated variance than the EWMA model.

d. A variance estimate from the GARCH(1,1) model is always between the prior day’s estimated variance and

the prior day’s squared return.

Correct answer: b

Explanation: The EWMA estimate of variance is a weighted average of the prior day’s variance and prior day

squared return.

Which of the following statements about the exponentially weighted moving average (EWMA) model and the generalized autoregressive conditional heteroscedasticity (GARCH(1,1)) model is correct?

a. The EWMA model is a special case of the GARCH(1,1) model with the additional assumption that the longrun volatility is zero.

b. A variance estimate from the EWMA model is always between the prior day’s estimated variance and the

prior day’s squared return.

c. The GARCH(1,1) model always assigns less weight to the prior day’s estimated variance than the EWMA model.

d. A variance estimate from the GARCH(1,1) model is always between the prior day’s estimated variance and

the prior day’s squared return.

Correct answer: b

Explanation: The EWMA estimate of variance is a weighted average of the prior day’s variance and prior day

squared return.

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